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Homework Help: Help with special relativity problem (off by a factor of 2)

  1. Jul 21, 2013 #1
    1. The problem statement, all variables and given/known data

    Special Relativity A.P French Problem 1-9

    An eccentric billionaire decides to sterilize his 106 liter swimming pool by boiling the water in it. For heating purposes he uses the fusion reaction:

    1H + 3H → 4He + radiant energy

    Assuming the heating system is 20% efficient, how much does he pay for the tritium (3H) to raise the pool temperature from 20°C to 100°C? It takes 4.2 joules to raise 1g of water through 1°C. Tritium costs about $5 per cm3 of gas at STP.

    2. Relevant equations

    E = mc2

    3. The attempt at a solution

    Total energy required:
    [tex] E_{total} = 4.2 \frac{J}{g°C} * 10^9 g * 80°C = 3.36*10^{11} J[/tex]

    Energy Generated per reaction:
    [tex] E_{reaction} = m_{diff} * c^{2}[/tex]
    [tex] E_{reaction} = ((1.0081 + 3.0170) - 4.0039)amu * 1.6603*10^{-27} * (3*10^{8}\frac{m}{s})^{2} = 3.1682 * 10^{-12} J [/tex]

    Atoms per cubic centimeter of gas at STP:

    [tex]\frac{atoms}{cm^3}=6.0221*10^{23} * \frac{1}{22.711} * 10^{-3} = 2.6516 * 10^{19}[/tex]

    Final Result (1/0.2) is to account for 20% efficiency:
    [tex]cost=$5*\frac{1}{0.2} * \frac{E_{total}}{\frac{E_{reaction}}{\frac{atoms}{cm^3}}} =~ $100,000[/tex]

    The answer in the book is $50,000, which would imply I'm off by a factor of two. I've looked over this for some time and can't see my mistake. Can anyone help me spot what I've missed?
    Last edited: Jul 21, 2013
  2. jcsd
  3. Jul 21, 2013 #2


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    Staff: Mentor

    It is "molecules per cubic centimeter", not atoms.

    Tritium gas is T2.

    That is a weird setup. He will spend the first billion (at least) for the fusion reactor.
  4. Jul 21, 2013 #3
    I think irrationality is a requirement in physics textbooks problems.

    Thanks for the help, that would certainly yield the right answer. Is this just something that should have been obvious from a chemistry standpoint? My chemistry is really rusty.
  5. Jul 22, 2013 #4


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    Hmm... it is something you should know, but there is a big difference between knowing it and thinking of it.
  6. Jul 22, 2013 #5
    Chemistry or physics, the thing to remember is that gases are made of molecules, and the Avogadro constant is how many molecules a mole of gas contains. Then you just need to find what a molecule of the given gas is.
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